Prove that If k, q, w and r are integers, and if c|k and c|q, then c|(kw + qr)

Q: 49. Let {x,}=1 be a sequence of real numbers such that xn Calculate lim,∞ exp(cos(x, – 1) – 1).…

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Q: 6. Use Stoke's Theorem to evaluate $F dr, where F =, and C is the part of the paraboloid z = 4 - x2…

A: Let F be a vector field and C be the boundary of the surface S. The Stoke's theorem states that…

Q: 5) Let f be a function of multiplicity 5 at p.Then at P, µ(x) = has multiplicity f'(x) f (x) A 4 B1…

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Q: Determine the general equation of the plane 2 passing through the point P(1,-4,-5) and parallel to…

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Q: 3 -2 7. Let u , and y . Let W = Span{, . -1 2 3 13 (a) Verify that {u,, ư2} is an orthogonal set.…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 1/3x^3/2,…

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Q: -3 Au = 3 and Av = -3 3 then A(-2u – 30) = %3D

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Q: Use the definition of the Laplace transform to compute L[f(t)]. For each, state the domain of…

A: The solution is given as

Q: A cylindrical water tank 6 meters high with a radius of 2 meters is buried so that the top of the…

A: The work done  in moving an object from one point to other is given by the product of weight of the…

Q: 4. Network flow is normally distributed with a mean of 570 bytes/packet and a standard deviation of…

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Q: Find the volume of the solid generated by revolving about the y-axis the region bounded by the curve…

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Q: For the following data (6, 6, 2, 2, 4, 4, 8, 2) , the mode equal 6 and 2 O 6 and 4 O 6 and 4 and 2 O…

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Q: Use the following definition of a Laplace transform. Let f be a function defined for t 2 0. Then the…

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Q: Payment of $882 due 1 month ago and $498 due today are to be repaid by a payment of $400 one month…

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Q: Assume thatf is differentiable in (-oo, x) and af'(r)N 0 for all a E (-00, 00). Prove that f has the…

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Q: The matrix A = -3 -2 -7| has an eigenvalue ) = -4. 1 3 ind an eigenvector for this eigenvalue. ry to…

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Q: The matrix A is a real symmetric 5 × 5 matrix with eigenvalues 2, 6, 11, 14, and 19. The vector æ1…

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Q: Let T and T' be topologies on a set X such that T' is strictly finer than T. If Y is a subset of X,…

A: The two topologies τ and τ' is defined on a set X. It is given that τ' is strictly finer than τ. By…

Q: 1 0 1 If B = -2 -2 -1 1 2 2 then det (B5) =

A: We have used determinant property.

Q: Given: 2a + 5b + 3c = 2 3a + b - 2c = 3 -a + 2b + c = 1 Identify the coefficient matri A and the…

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Q: 7. Esther, her mother and her grandmother have an average age of 53. Half of her grandmother's age,…

A: Let "x" be an age of Esther and "y" be an age of Esther mother and "z" be an age of Esther…

Q: Find the inverse Laplace transform of the function F(s)= (s- 4)e^-3s/(s^3 + 4s)

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Q: Answer both parts question 5 is only there cuz you need the problem to solve part a and part b…

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Q: OA. C1 J(5/9) (x) + c2J_(5/9) (x) B. Cį J(5/9) (x) + c2 Y(5/9) (x) OC. c J9/5) (x) + c2J_(9/5)(x) D.…

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Q: Let (G, ) denote the set of all 2 x 2 real matrices A with det{A} 0 Question 5. and det { A} € Q…

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Q: Find, i2509 7. :999 8. 5 :10 :15 +i •25 9. i' +i +i0 +i + i30 In each part, find z 10. z = 2+7i 11.…

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Q: exp(-4 + 5i) re2mi

A: According to Euler's Formula, for any real number x; eix=cos x+i sin x

Q: Consider the following. y = x2 y = 6- x 10 8 6 4 2- -2 4 (a) Find the area of the region by…

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Q: Solve for the determinant of matrix A below. * 3 2 A =|0 1 -2 1 3 4 O 16 O 25 О зо

A: Given matrix is A = 32101-2134

Q: According to Descartes' Rule of Signs, how many negative zeros could the polynomial -3z + 2x® – 2x2…

A: The number of possible negative real zeros is equal to the number of changes in the sign of the…

Q: Find the solutions of the system of inequalities by graphing: 2x – y 0

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Q: Solve and draw l sketch the graph of the polhowing equotions: x2 + ag? + z? 12y - 2z t 35 O 1. 2. 2…

A: The graph for equation 1 is shown in fig

Q: Assuming the roles of president and secretary cannot be filled by the same person, how many ways are…

A: When Tyler is chosen as president, we have 3 choices for the post of secretary. So there are 3 such…

Q: Solve xb =9 mod11

A: Solution:        As 11 is a prime number, by fermat's theorem,        x11-1 = 1 (mod 11)      =>…

Q: [1 2 1 21 21 2 1 et A = 1 2 1 2 [2 1 2 1. (a) (b) (c) Find all eigenvalues of A. Find a basis for…

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Q: A. Solve the following and show your solution. 1. Use the definition of Fibonacci numbers to find…

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Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: b) Consider the following Linear Programming problem: Min z = 2x, – 3x2 Subject to 1 1 z* +2 54 X1 +…

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Q: f) justify your conclusion) Coordinates of any points of inflection (State all points that you…

A: Given function is f(x)=x4+x3-2x2+2x2+x-2 Domain is -2<x<1 Point of inflection: For a given…

Q: Find the eigenvalues A1 < A2 < d3 and associated unit eigenvectors ủ1, ū2, ū3 of the symmetric…

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Q: Q1. Solue the intlial Valume Proklem mnd Ylo) -

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Q: Consider the definite integral 10 300x 1+ ex 1. Use the Trapezoidal Rule to estimate the value of…

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Q: Question no. 3 Use the inversion algorithm to find the inverse of the matrix (if the inverse…

A: Q3 asked and answered.

Q: Find the eigenvalues 11 < 12 < 13 and corresponding eigenvectors of the matrix

A: Given,          A=-5-201400-130005

Q: (-4,2+i, 1), and y = (i, 5, 1 + i) be vectors in C. Compute (r, y), Let z = ||x||, ||y||, and ||r+…

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Q: Show that the equation + 2k dy =c². possesses solutions of the form 00 2 c, e " cos (a, x + &,) cos…

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Q: d) TO e στοτ. OTO tionc of R?

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Q: Given P = R S²T0.5 + R0.5 S sin(2T) %3D P what is p ƏR O 3R S?T0.5 + 0.5R-0.5 sin(2T) O 2R³ ST0.5 +…

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Q: Write a in the form of a = a,T + ayN at t = 0 without finding T and N for r(t) = (2 + t)i + (t +…

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Q: Eight political committees must meet on the same day, but some members are on more than one…

A: Given- Eight political committees must meet on the same day, but some members are on more than one…